A while ago, I posted about some interesting problems posed in the Technology Review magazine.
- Jerry Grossman has equipped children with loaded water pistols and has them standing in an open field with no three of them in a straight line, such that the distances between pairs of them are distinct. At a given signal, each child shoots the closest other child with water. Show that if is any even number, then it is possible (but not necessarily the case) that every child gets wet. Show that if is odd, then necessarily at least one child stays dry.
Each of logicians A, B, and C wears a hat with a positive integer on it. The number on one hat is the sum of the numbers on the other two. The logicians take turns making statements, as follows:A: “I don’t know my number.”B: “My number is 15.”What numbers are on the hats of A and C?